Recent advancements in quantum computing have opened new avenues for tacklinglong-standing complex combinatorial optimization problems that are intractablefor classical computers. Predicting secondary structure of mRNA is one suchnotoriously difficult problem that can benefit from the ever-increasingmaturity of quantum computing technology. Accurate prediction of mRNA secondarystructure is critical in designing RNA-based therapeutics as it dictatesvarious steps of an mRNA life cycle, including transcription, translation, anddecay. The current generation of quantum computers have reached utility-scale,allowing us to explore relatively large problem sizes. In this paper, weexamine the feasibility of solving mRNA secondary structures on a quantumcomputer with sequence length up to 60 nucleotides representing problems in thequbit range of 10 to 80. We use Conditional Value at Risk (CVaR)-based VQEalgorithm to solve the optimization problems, originating from the mRNAstructure prediction problem, on the IBM Eagle and Heron quantum processors. Toour encouragement, even with ``minimal'' error mitigation and fixed-depthcircuits, our hardware runs yield accurate predictions of minimum free energy(MFE) structures that match the results of the classical solver CPLEX. Ourresults provide sufficient evidence for the viability of solving mRNA structureprediction problems on a quantum computer and motivate continued research inthis direction.